Adaptive
Regularization in Compressed Sensing Using the Discrepancy Principle

Compressed sensing images are usually reconstructed by
finding the minimum of an objective function with two terms: one that measures
the difference between the k-space data of the reconstructed image and the
measured k-space data (discrepancy term), and a term that measures the L1-norm
of the image in a sparsifying transform domain. A weighting factor
(regularization parameter) that must be properly chosen for good image quality,
balances the contribution of the two terms. A method called the discrepancy
principle automatically chooses the regularization parameter based on the size
of the discrepancy term and the measured noise in the k-space data.